How to set a fixed background image as reference for sculpting?
It is possible!

A few steps needed for it though.


You have to use a camera for this to work, the camera can be set up so the boundaries are at the edges of the screen, activating "lock camera to view" (function is in my favorites menu) makes it then possible to look around and rotate the view while staying in the camera.
After setting up the camera view, we need to add a background image or images to the camera, each image can be placed on the screen and scaled to our liking, allowing us to make a collage like in the mentioned video. If you made a collage of all the references already, fine, less images to load and position.
Under the camera object in the "Background Images" header we have the "Add Image" button. Clicking on that gives us a new entry "Not Set" under which we can Open/Select an image either from disk or use an already loaded one in the scene by using the little image icon with the arrow down, left to the "Open" button.
Once the image is loaded/selected, we have options like color space, alpha, depth (here we chose back) as well as frame method, where i would go with crop, to keep the image in ratio rather then stretching it. Further there is the X and Y offset which allows us to position the image(s) where we want them. Lastly rotation and scale for the fine tuning as well as options for vertical and horizontal flipping.
Once a picture is set up we can set up more by repeating the 3rd and 4th step, til we have all the screen estate used up. It is even possible to pack in more images that would lay on top of each other and show or hide them depending on their need.


Don't forget to save the file and eventually pack the images in the .blend file to open the file and realize the images are gone.

With all that said, here a little visual demonstration:



Excuse the small size, the 2MB upload limit forced me to cut down on size. Hope it still shows the essential part, that is, it works.